arXiv 1202.34182012-02-15cond-mat.quant-gasquant-ph

稀玻色-爱因斯坦凝聚体动力学方程中的碰撞积分

Collision Integrals in the Kinetic Equations of dilute Bose-Einstein Condensates

Erich D. Gust, L. E. Reichl

备注：: 17 pages

摘要：

本文推导了空间均匀玻色-爱因斯坦凝聚体中Bogoliubov激发动量分布的平均场动力学方程，着重讨论了碰撞积分。我们使用Peletminksii和Yatsenko的方法，而不是标准的非平衡格林函数形式主义。该方法产生三个碰撞积分${\cal G}^{12}$、${\cal G}^{22}$和${\cal G}^{31}$。之前的作者仅考虑了${\cal G}^{12}$和${\cal G}^{22}$。第三个碰撞积分${\cal G}^{31}$包含一个玻色子变成三个玻色子的过程的影响，反之亦然。这些过程是允许的，因为bogolons的总数不守恒。由于${\cal G}^{31}$与${\cal G}^{22}$的相互作用强度具有相同的数量级，因此我们预测它将显著影响bogolon气体的动力学，特别是bogolons总数向其平衡值的弛豫。

英文摘要：

We derive the mean field kinetic equation for the momentum distribution of Bogoliubov excitations (bogolons) in a spatially uniform Bose-Einstein condensate (BEC), with a focus on the collision integrals. We use the method of Peletminksii and Yatsenko rather than the standard non-equilibrium Green's function formalism. This method produces three collision integrals ${\cal G}^{12}$, ${\cal G}^{22}$ and ${\cal G}^{31}$. Only ${\cal G}^{12}$ and ${\cal G}^{22}$ have been considered by previous authors. The third collision integral ${\cal G}^{31}$ contains the effects of processes where one bogolon becomes three and vice versa. These processes are allowed because the total number of bogolons is not conserved. Since ${\cal G}^{31}$ is of the same order in the interaction strength as ${\cal G}^{22}$, we predict that it will significantly influence the dynamics of the bogolon gas, especially the relaxation of the total number of bogolons to its equilibrium value.

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